QJEEM21Ma730e: JEE Main 2021 Mathematics - Class 12 JEEM21Ma730e Solution: If the following system of linear equations 2x + y + z = 5 x −…

Question

Verified Solution • 2025–26 Session moderate

If the following system of linear equations

2x + y + z = 5

x

-

y + z = 3

x + y + az = b

has no solution, then :

Accepted Answer

Here

D = | \begin{matrix} 2 & 1 & 1 \\ 1 & - 1 & 1 \\ 1 & 1 & a \end{matrix} | \begin{matrix} = 2 (a - 1) - 1 (a - 1) + 1 + 1 \\ = 1 - 3 a \end{matrix}

D_{3} = | \begin{matrix} 2 & 1 & 5 \\ 1 & - 1 & 3 \\ 1 & 1 & b \end{matrix} | \begin{matrix} = 2 (- b - 3) - 1 (b - 3) + 5 (1 + 1) \\ = 7 - 3 b \end{matrix}

for

a = \frac{1}{3}, b \neq \frac{7}{3}

, system has no solutions.

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